Preheat the oven to 350 degrees F. Bring 1 quart of water to a boil. Add the walnuts and boil for 5 minutes. Drain. Return the saucepan to the stove and add sugar, 2 tablespoons of water, and the chile flakes. Stir the nuts until all the liquid disappears. Spread the nuts on a lined baking sheet, and place it in the preheated oven. Roast for about 15 minutes, turning them over after 7 minutes. Remove from the oven and cool down. Transfer to a airtight container or plastic bag.

Using vegetable peeler, peel the papayas, scrape off the seeds, and cut the papayas lengthwise into a 1/4-inch thick slices. Refrigerate.

Cut off the bottom of frisee, wash and separate the leaves. In a small bowl, combine all of the ingredients for the dressing. Stir until well mixed.

On 4 salad plates, place the frisee in the center. Arrange papaya slices on top of the leaves. Stir and drizzle the dressing over the frisee and papaya. Top the salad with some candied walnuts. Serve immediately.